## Doctoral Thesis

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For many years real-time task models have focused the timing constraints on execution windows defined by earliest start times and deadlines for feasibility.
However, the utility of some application may vary among scenarios which yield correct behavior, and maximizing this utility improves the resource utilization.
For example, target sensitive applications have a target point where execution results in maximized utility, and an execution window for feasibility.
Execution around this point and within the execution window is allowed, albeit at lower utility.
The intensity of the utility decay accounts for the importance of the application.
Examples of such applications include multimedia and control; multimedia application are very popular nowadays and control applications are present in every automated system.
In this thesis, we present a novel real-time task model which provides for easy abstractions to express the timing constraints of target sensitive RT applications: the gravitational task model.
This model uses a simple gravity pendulum (or bob pendulum) system as a visualization model for trade-offs among target sensitive RT applications.
We consider jobs as objects in a pendulum system, and the target points as the central point.
Then, the equilibrium state of the physical problem is equivalent to the best compromise among jobs with conflicting targets.
Analogies with well-known systems are helpful to fill in the gap between application requirements and theoretical abstractions used in task models.
For instance, the so-called nature algorithms use key elements of physical processes to form the basis of an optimization algorithm.
Examples include the knapsack problem, traveling salesman problem, ant colony optimization, and simulated annealing.
We also present a few scheduling algorithms designed for the gravitational task model which fulfill the requirements for on-line adaptivity.
The scheduling of target sensitive RT applications must account for timing constraints, and the trade-off among tasks with conflicting targets.
Our proposed scheduling algorithms use the equilibrium state concept to order the execution sequence of jobs, and compute the deviation of jobs from their target points for increased system utility.
The execution sequence of jobs in the schedule has a significant impact on the equilibrium of jobs, and dominates the complexity of the problem --- the optimum solution is NP-hard.
We show the efficacy of our approach through simulations results and 3 target sensitive RT applications enhanced with the gravitational task model.

The various uses of fiber-reinforced composites, for example in the enclosures of planes, boats and cars, generates the demand for a detailed analysis of these materials. The final goal is to optimize fibrous materials by the means of “virtual material design”. New fibrous materials are virtually created as realizations of a stochastic model and evaluated with physical simulations. In that way, materials can be optimized for specific use cases, without constructing expensive prototypes or performing mechanical experiments. In order to design a practically fabricable material, the stochastic model is first adapted to an existing material and then slightly modified. The virtual reconstruction of the existing material requires a precise knowledge of the geometry of its microstructure. The first part of this thesis describes a fiber quantification method by the means of local measurements of the fiber radius and orientation. The combination of a sparse chord length transform and inertia moments leads to an efficient and precise new algorithm. It outperforms existing approaches with the possibility to treat different fiber radii within one sample, with high precision in continuous space and comparably fast computing time. This local quantification method can be directly applied on gray value images by adapting the directional distance transforms on gray values. In this work, several approaches of this kind are developed and evaluated. Further characterization of the fiber system requires a segmentation of each single fiber. Using basic morphological operators with specific structuring elements, it is possible to derive a probability for each pixel describing if the pixel belongs to a fiber core in a region without overlapping fibers. Tracking high probabilities leads to a partly reconstruction of the fiber cores in non crossing regions. These core parts are then reconnected over critical regions, if they fulfill certain conditions ensuring the affiliation to the same fiber. In the second part of this work, we develop a new stochastic model for dense systems of non overlapping fibers with a controllable level of bending. Existing approaches in the literature have at least one weakness in either achieving high volume fractions, producing non overlapping fibers, or controlling the bending or the orientation distribution. This gap can be bridged by our stochastic model, which operates in two steps. Firstly, a random walk with the multivariate von Mises-Fisher orientation distribution defines bent fibers. Secondly, a force-biased packing approach arranges them in a non overlapping configuration. Furthermore, we provide the estimation of all parameters needed for the fitting of this model to a real microstructure. Finally, we simulate the macroscopic behavior of different microstructures to derive their mechanical and thermal properties. This part is mostly supported by existing software and serves as a summary of physical simulation applied to random fiber systems. The application on a glass fiber reinforced polymer proves the quality of the reconstruction by our stochastic model, as the effective properties match for both the real microstructure and the realizations of the fitted model. This thesis includes all steps to successfully perform virtual material design on various data sets. With novel and efficient algorithms it contributes to the science of analysis and modeling of fiber reinforced materials.